Correlation

by G. David Garson

A graduate-level illustrated introduction to and tutorial for Pearson correlation, Spearman's rank correlation (rho), Kendall's rank correlation (tau-b). polyserial correlation, biserial correlation, polychoric correlation, tetrachoric correlation, phi, point-biserial correlation, rank-biserial correlation (Somers' D), and more.New in the 2013 New and completely reworked sections on Pearson's, Spearman's, Kendall's, polyserial, polychoric, point biserial, rank biserial and phi correlations. Covers creation of appropriate correlation matrices for input to factor, structural equation modeling, and other procedures Covers SAS 9.3's new polyserial and polychoric correlation options. Covers SPSS, SAS, and Stata for all types of correlation. Shows how to reconcile output among statistical packages. Two dozen new illustrations. Below is the unformatted table of contents.CORRELATIONOverview6Deviation7Covariance8Standardization8Data example8Pearson correlation (for interval data)10Coefficient of determination, r210Attenuation of correlation11Spearman's rho (for ordinal data)26Kendall's tau-b (for ordinal data)29Polyserial correlation (for a continuous with an ordinal or binary variable)32Polychoric correlation (for ordinal and binary variables)34Other software for polychoric correlation40Phi (for two binary variables)40Other types of correlation41Point-biserial correlation41Converting point-biserial to biserial correlation42Rank-biserial correlation (Somers' D)42Correlation ratio, eta46Coefficient of intraclass correlation (ICC)46Assumptions46Frequently Asked Questions49Do I want one-tailed or two-tailed significance?49How many correlations will there be among k variables?49How do I convert correlations into z scores?50How is the significance of a Pearson correlation coefficient computed?53Significance of r53Significance of the difference between two correlations from two independent samples53Significance of the difference between two dependent correlations from the same sample54How do I set confidence limits on my correlation coefficients?55I have ordinal variables and thus used Spearman's rho. How do I use these ordinal correlations in SPSS for partial correlation, regression, and other procedures?55Are polyserial and biserial correlations simply Spearman's rho applied to appropriate variables?55What is the relation of correlation to ANOVA?56What is the relation of correlation to validity?56 60

68 pages, Kindle Edition

First published April 17, 2012